You create a batch file containing the instructions to rename the backup image.
You then put that file name in the Pre/Post command option of your backup task.
The backup finishes, the batch file is executed and renames the image file.

As TheWeaz said you could use batch file which deletes or renames backups as a pre\post-backup command. This Acronis Public Knowledge Base article provides the instructions on how to rename backups in accordance with the current date.

You can find the detailed instructions on how to use pre/post commands in section 5.3.3. in the Acronis True Image 10.0 Home User's Guide.

I use ATI 10 to automatically run scehduled complete backups (not inc or diff files) everyday. ATI10 automatically names the files uniquely, incorporoating date and time into the backup file name.

This is easy to do in ATI 10 with the Managed Backup Location Feature. From the main screen pick the category called "BAckup Locations" and create directory and set the limits you choose. The create a scheduled task to back up MY Data, select the files you want backup up, specificy, choose for the destination Backup Locations form the tree in the left window, then selct the directory you created. Set to make Full Backups, and set to run as often as you like.